01 生成 Thue–Morse 序列Generate Thue–Morse Sequence
生成 Thue–Morse 序列：n 的二进制中 1 的个数的奇偶（0/1）。本地处理。可设置「项数」、「每行一个」。Generate the Thue–Morse sequence: parity of the number of 1-bits in n (0/1). Processed locally. Settings: Terms, One per line.
使用说明与常见问题How-to & FAQ
「生成 Thue–Morse 序列」是什么？What is the Generate Thue–Morse Sequence tool?
生成 Thue–Morse 序列：n 的二进制中 1 的个数的奇偶（0/1）。本地处理。可设置「项数」、「每行一个」。Generate the Thue–Morse sequence: parity of the number of 1-bits in n (0/1). Processed locally. Settings: Terms, One per line.
如何使用「生成 Thue–Morse 序列」？How do I use the Generate Thue–Morse Sequence tool?
在「生成 Thue–Morse 序列」中，按需设置「项数」，结果会实时显示在下方，点击「复制结果」即可复制。In the Generate Thue–Morse Sequence: Adjust "Terms"; the result appears below instantly — click "Copy result" to copy it.
为什么说 Thue–Morse 序列不含立方？Why is the Thue–Morse sequence called cube-free?
序列里不会出现同一片段连续重复三次的 xxx（例如 000 或 010101），它甚至不含 axaxa 形式的重叠。第 n 项等于 n 的二进制中 1 的个数的奇偶（0 为偶，1 为奇）。No block ever appears three times in a row as xxx (such as 000 or 010101); it does not even contain overlaps of the form axaxa. Term n is the parity of the number of 1s in the binary form of n (0 = even, 1 = odd).
输入和输出是什么样的？What does the input and output look like?
例如在「生成 Thue–Morse 序列」中把「项数」设为 8，输出为：0 1 1 0 1 0 0 1。For example, in the Generate Thue–Morse Sequence with "Terms" set to 8, the output is: 0 1 1 0 1 0 0 1.
有哪些选项可以调整？What options can I adjust?
「生成 Thue–Morse 序列」的设置：「项数」默认 32；可勾选：「每行一个」。每次生成结果都按当前设置处理。Settings in the Generate Thue–Morse Sequence — "Terms" default 32; tick boxes: "One per line". The result always uses the current settings.
计算精度如何？How precise are the results?
「生成 Thue–Morse 序列」输出的每一项都是精确的整数（只有 0 和 1，按二进制中 1 的个数的奇偶得到），计算中没有舍入，也不涉及浮点精度问题。Every term the Generate Thue–Morse Sequence outputs is an exact integer (only 0 and 1, from the parity of the number of 1 bits); there is no rounding and floating-point precision never comes into play.
「生成 Thue–Morse 序列」免费吗？需要注册吗？Is the Generate Thue–Morse Sequence free? Do I need an account?
「生成 Thue–Morse 序列」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Generate Thue–Morse Sequence is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.